Product is the name of many different concepts in mathematics. In arithmetic, the result of multiplication of two or more numbers is called their product or product.
When the multiplied numbers are real numbers or complex numbers, the order of multiplication has no effect on the product, which is called commutativity. When the product is a quaternion or matrix, or an element in some algebraic structures, the order will affect the result of the product. This shows that the multiplication of these objects is not commutative.
When more than two objects need to be multiplied, the multiplication symbol ∏ (capital π) is often used. Just like adding multiple objects with sigma as the symbol. Generally speaking, when only one object is to be multiplied, the product is the object itself; The so-called "empty product" can also be agreed to be 1 without multiplication objects.
Algebraic definition:
The concept of product depends on the definition of "multiplication". When people upgrade the set of multiplication objects to more general sets, such as groups, rings, fields, etc. The concept of the product will also change.
Let A be a set, we define the multiplication F:A ×A→A, that is, the mapping of A and its own cartesian product to A, and let (x, y)∈A×A, then we call the pixel F(x, y) the product of x and y, abbreviated as xy.